可压缩Navier-Stokes-Cahn-Hilliard方程组描述了互不相溶两相流体的流动，是两相流体动力学的一个重要模型，具有强非线性性、退化性和奇异性。本项目主要研究可压缩Navier-Stokes-Cahn-Hilliard方程组解的适定性以及大时间行为。特别地，我们将研究：1. 混有运动刚体的三维有界区域中，可压缩等熵Navier-Stokes-Cahn-Hilliard方程组的广义Navier初边值问题；2. 可压缩非等熵Navier-Stokes-Cahn-Hilliard方程组的Cauchy问题。

The compressible Navier-Stokes-Cahn-Hilliard system describing the two-phase flow of immicible fluids, is an important model in two-phase fluid dynamics, with strong non-linearity, degeneracy and singularity. We are mainly concerned with the well-posedness and large-time behavior of the solutions to this system. In particular, we will study: 1. the generalized Navier initial-boundary value problem of 3D isentropic compressible Navier-Stokes-Cahn-Hilliard system in a bounded domain with rigid bodies in motion; and 2. the Cauchy problem of non-isentropic compressible Navier-Stokes-Cahn-Hilliard system.